Solve 4:(sqrt{48}+1/4sqrt{12})divsqrt{27}=

$$4 : ( \sqrt { 48 } + \frac { 1 } { 4 } \sqrt { 12 } ) \div \sqrt { 27 } =$$

Evaluate

$$\frac{8}{81}\approx 0.098765432$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{\frac{4}{4\sqrt{3}+\frac{1}{4}\sqrt{12}}}{\sqrt{27}}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{\frac{4}{4\sqrt{3}+\frac{1}{4}\times 2\sqrt{3}}}{\sqrt{27}}$$

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

$$\frac{\frac{4}{4\sqrt{3}+\frac{2}{4}\sqrt{3}}}{\sqrt{27}}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{4}{4\sqrt{3}+\frac{1}{2}\sqrt{3}}}{\sqrt{27}}$$

Combine 4\sqrt{3} and \frac{1}{2}\sqrt{3} to get \frac{9}{2}\sqrt{3}.

$$\frac{\frac{4}{\frac{9}{2}\sqrt{3}}}{\sqrt{27}}$$

Rationalize the denominator of \frac{4}{\frac{9}{2}\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\frac{4\sqrt{3}}{\frac{9}{2}\left(\sqrt{3}\right)^{2}}}{\sqrt{27}}$$

The square of \sqrt{3} is 3.

$$\frac{\frac{4\sqrt{3}}{\frac{9}{2}\times 3}}{\sqrt{27}}$$

Express \frac{9}{2}\times 3 as a single fraction.

$$\frac{\frac{4\sqrt{3}}{\frac{9\times 3}{2}}}{\sqrt{27}}$$

Multiply 9 and 3 to get 27.

$$\frac{\frac{4\sqrt{3}}{\frac{27}{2}}}{\sqrt{27}}$$

Divide 4\sqrt{3} by \frac{27}{2} by multiplying 4\sqrt{3} by the reciprocal of \frac{27}{2}.

$$\frac{\frac{4\sqrt{3}\times 2}{27}}{\sqrt{27}}$$

Multiply 4 and 2 to get 8.

$$\frac{\frac{8\sqrt{3}}{27}}{\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{\frac{8\sqrt{3}}{27}}{3\sqrt{3}}$$

Express \frac{\frac{8\sqrt{3}}{27}}{3\sqrt{3}} as a single fraction.

$$\frac{8\sqrt{3}}{27\times 3\sqrt{3}}$$

Cancel out \sqrt{3} in both numerator and denominator.

$$\frac{8}{3\times 27}$$

Multiply 3 and 27 to get 81.

$$\frac{8}{81}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {4}} = 0.09876543209876543$$